Source depth discrimination with a vertical line array

Abstract

Source depth estimation with a vertical line array generally involves mode filtering, then matched-mode processing. Because mode filtering is an ill-posed problem if the water column is not well-sampled, concerns for robustness motivate a simpler approach: source depth discrimination considered as a binary classification problem. It aims to evaluate whether the source is near the surface or submerged. These two hypotheses are formulated in terms of normal modes, using the concept of trapped and free modes. Decision metrics based on classic mode filters are proposed. Monte Carlo methods are used to predict performance and set the parameters of a classifier accordingly.

Depth Discrimination for Low-Frequency Sources Using a Horizontal Line Array of Acoustic Vector Sensors Based on Mode Extraction

“…However, SI can be used to discriminate source depth only if those ranges are sufficiently close, since it is influenced by the source-receiver range besides source depth. Considering the ill-posed problem of mode filtering when the water column is not well-sampled by the VLA, Conan et al [9] proposed a robust method for discriminating the source depth supported by previous work introduced in [6,7,8]. When the VLA spans only 50% of the water column, that method outperforms those proposed in [6,7], as is evaluated by the receiver operating characteristic curve.…”

“…After estimating the source depth $z_{\mathrm{s}}$, a depth threshold $z_0$ (usually 5–10 m) is set to determine whether a source is shallow or deep. The source discrimination problem can be addressed as [9] $\begin{array}{c}{H}_0:z_s\le z_0\\ H_1:z_s>z_0.\end{array}$…”

“…We assume that the physical quantity can be expressed as $Rfalse(z_{s}false)$. Therefore, the source-discrimination model is written as [9] $\begin{array}{c}{H}_0:R(z_{\mathrm{normals}})\le \eta \\ H_1:R(z_{\mathrm{normals}})>\eta \end{array}$where $\eta$ is the decision threshold. Herein, we propose the depth-discrimination method based on the second framework.…”

“…Using the estimation of modal amplitudes ${\hat{d}}_{\mathrm{p}}={false[{\widehat{d}}_{\mathrm{normalp}1},\cdots ,{\widehat{d}}_{\mathrm{normalp}M}false]}^T$ and ${\hat{d}}_{\mathrm{v}}={false[{\widehat{d}}_{\mathrm{normalv}1},\cdots ,{\widehat{d}}_{\mathrm{normalv}M}false]}^T$ by the mode-extraction method, $\hat{R}false(z_{s}false)=\frac{true\sum _{m=1}^{m_0}{\widehat{d}}_{\mathrm{normalp}m}false(r,z_{\mathrm{s}}false)\cdot {\widehat{d}}_{\mathrm{normalv}m}^{*}false(r,z_{\mathrm{s}}false)}{true\sum _{m=1}^M{\widehat{d}}_{\mathrm{normalp}m}false(r,z_{\mathrm{s}}false)\cdot {\widehat{d}}_{\mathrm{normalv}m}^{*}false(r,z_{\mathrm{s}}false)}$where $m_0$ is the number of low-order modes. The low-order modes are defined as those with phase speeds lower than the maximum sound speed in the water column [9], and $m_0$ is determined by $c_{\mathrm{normalp}}(m_0)<c_{\max },c_{\mathrm{normalp}}(m_0+1)>c_{\max }$where $c_{\mathrm{p}}false(mfalse)$ is the phase speed of the mode of order m , and $c_{\max }$ is the maximum sound speed. In this case, Modes 1–9 are the low-order modes and the rest are the high-order modes.…”

“…However, the frequency of the moving source must be known a priori, which is difficult with passive sonar system. Next, unlike the first approach based on depth estimation, the second approach considers depth discrimination as a binary hypothesis test; examples include the matched-subspace method [6,7], the scintillation index (SI) [8], and the trapped energy ratio [9] to improve the robustness of depth discrimination.…”